Define GenPastro

This commit is contained in:
Kiana Sheibani 2023-03-06 10:51:03 -05:00
parent ac292d092e
commit c6215d7509
Signed by: toki
GPG key ID: 6CB106C25E86A9F7

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@ -72,3 +72,61 @@ ungentambara f x = dimap unitr.bwd unitr.fwd $ getTambara $ f x
public export
Tambara : (p : Type -> Type -> Type) -> Type
Tambara = GenTambara Pair
-- Pastro
public export
data GenPastro : (ten, p : Type -> Type -> Type) -> Type -> Type -> Type where
MkPastro : (y `ten` z -> b) -> p x y -> (a -> x `ten` z) -> GenPastro ten p a b
export
Profunctor (GenPastro ten p) where
dimap f g (MkPastro l m r) = MkPastro (g . l) m (r . f)
lmap f (MkPastro l m r) = MkPastro l m (r . f)
rmap g (MkPastro l m r) = MkPastro (g . l) m r
export
ProfunctorFunctor (GenPastro ten) where
promap f (MkPastro l m r) = MkPastro l (f m) r
export
(Tensor ten i, Symmetric ten) => ProfunctorMonad (GenPastro ten) where
propure x = MkPastro unitr.fwd x unitr.bwd
projoin (MkPastro {x=x',y=y',z=z'} l' (MkPastro {x,y,z} l m r) r') = MkPastro ll m rr
where
ll : y `ten` (z' `ten` z) -> b
ll = l' . mapFst l . assoc.fwd . mapSnd swap
rr : a -> x `ten` (z' `ten` z)
rr = mapSnd swap . assoc.bwd . mapFst r . r'
export
ProfunctorAdjunction (GenPastro ten) (GenTambara ten) where
prounit x = MkTambara (MkPastro id x id)
procounit (MkPastro l (MkTambara x) r) = dimap r l x
export
(Associative ten, Symmetric ten) => GenStrong ten (GenPastro ten p) where
strongl (MkPastro {x,y,z} l m r) = MkPastro l' m r'
where
l' : y `ten` (z `ten` c) -> b `ten` c
l' = mapFst l . assoc.fwd
r' : a `ten` c -> x `ten` (z `ten` c)
r' = assoc.bwd . mapFst r
strongr (MkPastro {x,y,z} l m r) = MkPastro l' m r'
where
l' : y `ten` (c `ten` z) -> c `ten` b
l' = swap . mapFst l . assoc.fwd . mapSnd swap
r' : c `ten` a -> x `ten` (c `ten` z)
r' = mapSnd swap . assoc.bwd . mapFst r . swap
export
genpastro : GenStrong ten q => p :-> q -> GenPastro ten p :-> q
genpastro @{gs} f (MkPastro l m r) = dimap r l (strongl @{gs} (f m))
export
ungenpastro : Tensor ten i => GenPastro ten p :-> q -> p :-> q
ungenpastro f x = f (MkPastro unitr.fwd x unitr.bwd)